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We investigate two efficient time discretizations for the post-processing technique of discontinuous Galerkin (DG) methods to solve hyperbolic conservation laws. The post-processing technique, which is applied at the final time of the DG method, can enhance the accuracy of the original DG solution (spatial superconvergence). One main difficulty of the post-processing technique is that the spatial superconvergence after post-processing needs to be matched with proper temporary accuracy. If the semi-discretized system (ODE system after spatial discretization) is under-resolved in time, then the space superconvergence will be concealed. In this paper, we focus our investigation on the recently designed SDG method and derive its explicit scheme from a correction process based on the DG weak formulation. We also introduce another similar technique, namely the spectral deferred correction (SDC) method. A comparison is made among both proposed time discretization techniques with the standard third-order Runge-Kutta method through several numerical examples, to conclude that both the SDG and SDC methods are efficient time discretization techniques for exploiting the spatial superconvergence of the DG methods.

Formally verifying the properties of formal systems using a proof assistant requires justifying numerous minor lemmas about capture-avoiding substitution. Despite work on category-theoretic accounts of syntax and variable binding, raw, first-order representations of syntax, the kind considered by many practitioners and compiler frontends, have received relatively little attention. Therefore applications miss out on the benefits of category theory, most notably the promise of reusing formalized infrastructural lemmas between implementations of different systems. Our Coq framework Tealeaves provides libraries of reusable infrastructure for a raw, locally nameless representation and can be extended to other representations in a modular fashion. In this paper we give a string-diagrammatic account of decorated traversable monads (DTMs), the key abstraction implemented by Tealeaves. We define DTMs as monoids of structured endofunctors before proving a representation theorem a la Kleisli, yielding a recursion combinator for finitary tree-like datatypes.

Intelligent transportation systems play a crucial role in modern traffic management and optimization, greatly improving traffic efficiency and safety. With the rapid development of generative artificial intelligence (Generative AI) technologies in the fields of image generation and natural language processing, generative AI has also played a crucial role in addressing key issues in intelligent transportation systems, such as data sparsity, difficulty in observing abnormal scenarios, and in modeling data uncertainty. In this review, we systematically investigate the relevant literature on generative AI techniques in addressing key issues in different types of tasks in intelligent transportation systems. First, we introduce the principles of different generative AI techniques, and their potential applications. Then, we classify tasks in intelligent transportation systems into four types: traffic perception, traffic prediction, traffic simulation, and traffic decision-making. We systematically illustrate how generative AI techniques addresses key issues in these four different types of tasks. Finally, we summarize the challenges faced in applying generative AI to intelligent transportation systems, and discuss future research directions based on different application scenarios.

This paper presents a novel solution to address the challenges in achieving energy efficiency and cooperation for collision avoidance in UAV swarms. The proposed method combines Artificial Potential Field (APF) and Particle Swarm Optimization (PSO) techniques. APF provides environmental awareness and implicit coordination to UAVs, while PSO searches for collision-free and energy-efficient trajectories for each UAV in a decentralized manner under the implicit coordination. This decentralized approach is achieved by minimizing a novel cost function that leverages the advantages of the active contour model from image processing. Additionally, future trajectories are predicted by approximating the minima of the novel cost function using calculus of variation, which enables proactive actions and defines the initial conditions for PSO. We propose a two-branch trajectory planning framework that ensures UAVs only change altitudes when necessary for energy considerations. Extensive experiments are conducted to evaluate the effectiveness and efficiency of our method in various situations.

Code writing is repetitive and predictable, inspiring us to develop various code intelligence techniques. This survey focuses on code search, that is, to retrieve code that matches a given query by effectively capturing the semantic similarity between the query and code. Deep learning, being able to extract complex semantics information, has achieved great success in this field. Recently, various deep learning methods, such as graph neural networks and pretraining models, have been applied to code search with significant progress. Deep learning is now the leading paradigm for code search. In this survey, we provide a comprehensive overview of deep learning-based code search. We review the existing deep learning-based code search framework which maps query/code to vectors and measures their similarity. Furthermore, we propose a new taxonomy to illustrate the state-of-the-art deep learning-based code search in a three-steps process: query semantics modeling, code semantics modeling, and matching modeling which involves the deep learning model training. Finally, we suggest potential avenues for future research in this promising field.

The position estimation problem based on received power measurements is investigated for visible light systems in the presence of luminous flux degradation of light emitting diodes (LEDs). When the receiver is unaware of this degradation and performs position estimation accordingly, there exists a mismatch between the true model and the assumed model. For this scenario, the misspecified Cram\'er-Rao bound (MCRB) and the mismatched maximum likelihood (MML) estimator are derived to quantify the performance loss due to this model mismatch. Also, the Cram\'er-Rao lower bound (CRB) and the maximum likelihood (ML) estimator are derived when the receiver knows the degradation formula for the LEDs but does not know the decay rate parameter in that formula. In addition, in the presence of full knowledge about the degradation formula and the decay rate parameters, the CRB and the ML estimator are obtained to specify the best achievable performance. By evaluating the theoretical limits and the estimators in these three scenarios, we reveal the effects of the information about the LED degradation model and the decay rate parameters on position estimation performance. It is shown that the model mismatch can result in significant degradation in localization performance at high signal-to-noise ratios, which can be compensated by conducting joint position and decay rate parameter estimation.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

Knowledge graphs represent factual knowledge about the world as relationships between concepts and are critical for intelligent decision making in enterprise applications. New knowledge is inferred from the existing facts in the knowledge graphs by encoding the concepts and relations into low-dimensional feature vector representations. The most effective representations for this task, called Knowledge Graph Embeddings (KGE), are learned through neural network architectures. Due to their impressive predictive performance, they are increasingly used in high-impact domains like healthcare, finance and education. However, are the black-box KGE models adversarially robust for use in domains with high stakes? This thesis argues that state-of-the-art KGE models are vulnerable to data poisoning attacks, that is, their predictive performance can be degraded by systematically crafted perturbations to the training knowledge graph. To support this argument, two novel data poisoning attacks are proposed that craft input deletions or additions at training time to subvert the learned model's performance at inference time. These adversarial attacks target the task of predicting the missing facts in knowledge graphs using KGE models, and the evaluation shows that the simpler attacks are competitive with or outperform the computationally expensive ones. The thesis contributions not only highlight and provide an opportunity to fix the security vulnerabilities of KGE models, but also help to understand the black-box predictive behaviour of KGE models.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.